Abstract
Line conjugates and (B)line conjugates are defined. Associated points, lines, conics, and cubics are introduced and investigated in the context of functional equations. Triangle centers and central lines are treated as functions of the sidelengths a, b, c of a variable reference triangle ABC. Relationships usually regarded as geometric are regarded as algebraic (e.g. collinearity of points, concurrence of lines, perspectivity of triangles). The methods depend on homogeneous barycentric (or trilinear) coordinates.
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Kimberling, C., Moses, P.J.C. Line conjugates in the plane of a triangle. Aequat. Math. 97, 161–184 (2023). https://doi.org/10.1007/s00010-022-00905-2
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DOI: https://doi.org/10.1007/s00010-022-00905-2